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It has been decades since the academic world of ruin theory defined the insolvency of an insurance company as the time when its surplus falls below zero. This simplification, however, needs careful adaptions to imitate the real-world…

Risk Management · Quantitative Finance 2020-07-06 Aili Zhang , Ping Chen , Shuanming Li , Wenyuan Wang

The insurance model when the amount of claims depends on the state of the insured person (healthy, ill, or dead) and claims are connected in a Markov chain is investigated. The signed compound Poisson approximation is applied to the…

Probability · Mathematics 2020-01-13 Gabija Liaudanskaitė , Vydas Čekanavičius

In this note, we study the ultimate ruin probabilities of a real-valued L{\'e}vy process X with light-tailed negative jumps. It is well-known that, for such L{\'e}vy processes, the probability of ruin decreases as an exponential function…

Probability · Mathematics 2018-02-26 Jérôme Spielmann

Competing and Complementary risk (CCR) problems are often modelled using a class of distributions of the maximum, or minimum, of a random number of i.i.d. random variables; we call this class the CCR class of distributions. While the CCR…

Probability · Mathematics 2025-10-21 Anum Fatima , Gesine Reinert

We consider in this paper a general two-sided jump-diffusion risk model that allows for risky investments as well as for correlation between the two Brownian motions driving insurance risk and investment return. We first introduce the model…

Computational Finance · Quantitative Finance 2013-02-28 Chuancun Yin , Yuzhen Wen

With the ubiquitous availability of unstructured data, growing attention is paid as how to adjust for selection bias in such non-probability samples. The majority of the robust estimators proposed by prior literature are either fully or…

Methodology · Statistics 2022-04-08 Ali Rafei , Michael R. Elliott , Carol A. C. Flannagan

In this article we consider the surplus process of an insurance company within the Cramer-Lundberg framework. We study the optimal reinsurance strategy and dividend distribution of an insurance company under proportional reinsurance, in…

Optimization and Control · Mathematics 2026-05-22 Zakaria Aljaberi , Asma Khedher , Mohamed Mnif

We examine hitting probability problems for Ornstein-Uhlenbeck (OU) processes and Geometric Brownian motions (GBM) with respect to exponential boundaries related to problems arising in risk theory and asset and liability models in pension…

Probability · Mathematics 2023-12-14 Efstathia Bougioukli , Michael A. Zazanis

Most risk analysis models systematically underestimate the probability and impact of catastrophic events (e.g., economic crises, natural disasters, and terrorism) by not taking into account interconnectivity and interdependence of risks. To…

Physics and Society · Physics 2017-10-17 Xin Lin , Alaa Moussawi , Gyorgy Korniss , Jonathan Z. Bakdash , Boleslaw K. Szymanski

In this paper, we study finite-time ruin probabilities for the compound Markov binomial risk model - a discrete-time model where claim sizes are modulated by a finite-state ergodic Markov chain. In the classic (non-modulated) case, the risk…

Probability · Mathematics 2025-07-23 Zbigniew Palmowski , Lewis Ramsden , Apostolos D. Papaioannou

In this paper, we introduce a risk process, namely, the mixed fractional risk process (MFRP) in which the number of claims in the associated claim process are modelled using the mixed fractional Poisson process (MFPP). The covariance…

Probability · Mathematics 2021-06-23 K. K. Kataria , M. Khandakar

We introduce the concept of cumulative Parisian ruin, which is based on the time spent in the red by the underlying surplus process. Our main result is an explicit representation for the distribution of the occupation time, over a…

Probability · Mathematics 2015-09-24 Hélène Guérin , Jean-François Renaud

In this work, we propose a simplification of the Pollaczek-Khinchine formula for the ultimate time survival (or ruin) probability calculation in exchange for a few assumptions on the random variables which generate the renewal risk model.…

Probability · Mathematics 2024-01-08 Andrius Grigutis

Consider a multi-dimensional Brownian motion which models the surplus processes of multiple lines of business of an insurance company. Our main result gives exact asymptotics for the cumulative Parisian ruin probability as the initial…

Probability · Mathematics 2020-04-28 Lanpeng Ji

A high order expansion of the renewal function is provided under the assumption that the inter-renewal time distribution is light tailed with finite moment generating function g on a neighborhood of 0. This expansion relies on complex…

Probability · Mathematics 2016-11-29 Clément Dombry , Landy Rabehasaina

We derive a closed-form (infinite series) representation for the distribution of the ruin time for the Sparre Andersen model with exponentially distributed claims. This extends a recent result of Dickson et al. (2005) for such processes…

Probability · Mathematics 2007-09-07 K. A. Borovkov , D. C. M. Dickson

In this paper, we introduce an insurance ruin model with adaptive premium rate, thereafter refered to as restructuring/refraction, in which classical ruin and bankruptcy are distinguished. In this model, the premium rate is increased as…

Probability · Mathematics 2013-06-21 Jean-François Renaud

In this paper, we investigate the ruin probabilities of non-homogeneous risk models. By employing martingale method, the Lundberg-type inequalities of ruin probabilities of non-homogeneous renewal risk models are obtained under weak…

Probability · Mathematics 2020-06-05 Qianqian Zhou , Alexander Sakhanenko , Junyi Guo

In this paper, we consider the perturbed renewal risk process. Systems of integro-differential equations for the Gerber-Shiu functions at ruin caused by a claim and oscillation are established, respectively. The explicit Laplase transforms…

Probability · Mathematics 2008-03-07 Min Song

We study an optimal dividend problem for an insurer who simultaneously controls investment weights in a financial market, liability ratio in the insurance business, and dividend payout rate. The insurer seeks an optimal strategy to maximize…

Mathematical Finance · Quantitative Finance 2021-05-27 Zhuo Jin , Zuo Quan Xu , Bin Zou